Drupal - How to get paragraph field values?

You should be able to include the Paragraph entity class, and use Paragraph::load($entity_id) to load it.

Example:

use Drupal\paragraphs\Entity\Paragraph;

$paragraph = Paragraph::load($target_id);
$foo = $paragraph->field_name->value;

$paragraph = Paragraph::load($target_id);
// Paragraph type could be also useful.
$prgTypeId = $paragraph->getType();
/** @var \Drupal\Core\Field\EntityReferenceFieldItemList $prgMediaField */
$prgMediaField = $paragraph->get('field_media');
$prgMediaFieldValue = $prgMediaField->getValue();

I know this is old, but might be helpful for the future. To load entities referenced by a Node entity you can use the entity property. For example, consider the following code:

$nodestorage = \Drupal::entityManager()->getStorage('node');
$node = $nodestorage->loadUnchanged(9);

foreach ($node->field_products as $product) {

  /** @var Entity (i.e. Node, Paragraph, Term) $referenced_product **/
  $referenced_product = $product->entity;

  // Use now the entity to get the values you need.
  $field_value = $referenced_product->field_name->value;
}

So no need to load an entity by the entity id, you just simply user ->entity property over a referenced list of entities.